//1.原数组操作
class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        for(int i = 1;i<m;++i) {
            grid[i][0] = grid[i][0] + grid[i-1][0];
        }
        for(int j = 1; j< n;++j)  {
            grid[0][j] = grid[0][j] + grid[0][j-1];
        }
        for(int i = 1;i<m;++i) {
            for(int j = 1; j< n;++j) {
                grid[i][j] = grid[i][j] + min(grid[i-1][j], grid[i][j-1]);
            }

        }
        return grid[m-1][n-1];
    }
};

//2.额外数组操作
class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        vector<vector<int>> dp(m,vector<int>(n,1));
        dp[0][0]=grid[0][0];
        for(int i = 1;i<m;++i) {
            dp[i][0] = grid[i][0] + dp[i-1][0];
        }
        for(int j = 1; j< n;++j)  {
            dp[0][j] = grid[0][j] + dp[0][j-1];
        }
        for(int i = 1;i<m;++i) {
            for(int j = 1; j< n;++j) {
                dp[i][j] = grid[i][j] + min(dp[i-1][j], dp[i][j-1]);
            }

        }
        return dp[m-1][n-1];
    }
};





